Would an SSD solve my occasional system hang with database usage?

A standard workstation that I usually use will come with two HDD. OS/programs will be on the primary HDD and the data files/DB2 databases will be on the secondary HDD. Storage capacity has rarely been an issue and performance with the system and databases has always been responsive with no issues.

My issues began to rise when I was moved over to a 14" ultra book where only a single HDD can be used. I have the HDD split into two partitions. One for OS/programs and the other for data files and databases (Because the in-house programs that I use require separate drive letters for caching, system files, and storage of temp files.) Whenever I use the programs to read and write data to the database. My system will hang with the HDD/activity light pinned on and the mouse cursor displaying the "busy" cursor and this can take up to 10-15 minutes just to do one task. If I do everything off of the database (for example, using VPN to offload onto company servers) no performance issues.

The last workstation that I last used came with a SSD for a primary drive and a HDD for a secondary drive. Instead of the usual, OS/programs on primary and files/databases on secondary. We decided to put the database onto the SSD with the OS/programs and used the secondary drive for data files, etc. Again, no performance issues whatsoever.

I was under the assumption that the reason why I was experiencing these issues was because I was using a HDD and the HDD might be reading/writing at the same time and this was causing my system to bottleneck.

Would a SSD solve the issues that I am having? Can a SSD handle reading/writing at the same time?

This would save me a ton of time instead of waiting/dealing with the company in getting another workstation sent to my residence. And would also explain why having the DB2 database on the SSD on my last workstation never had any performance issues.

I don't believe my system is the issue. It is running a PM45 chipset with an Intel Core 2 Duo T9600 2.8GHz processor and 4GB DDR2 800 RAM.

Yes, an SSD would work wonders in that situation. See, whats happening is that the database program is requesting a crapload of read/writes from the mechanical drive, but the problem is that the drive has to move the read/write arm back and forth to perform those actions.
So when a burst of requests reach the drive, it starts thrashing to feed the demand, with each request taking a minimum of ~8-10ms for the arm and the disk to move into position for access.

With an SSD on the other hand, nothing moves, and the requested data can be read near instantly (~20-50 nanoseconds), because as far as the drive is concerned all of the data is sequential. So a 5000 data point access on a mechanical that would take several minutes for it to churn through would take under a second for an SSD.
On top of the high random read performance, the drive can under the proper conditions maintain its normal throughput performance even with high random read/write.